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This question is in the book of Mark Allen Weiss in exerice 10 in chapter 6 about heaps.

Could you please help me to solve this problem? enter image description here

I was able to find a solution that gives a 3N/4 comparison in most cases, but there is cases where my algorithm do N comparasions.

In my solution, I start from the level before last and I check if I have to go up (if X < minimum of the level) which gives N/2 comparisons, or I have to go down (if X > maximum of the level) which gives 3N/4 comparisons. But when X is between the min and max of the penultimate level I can't decide whether to go up or down which gives N comparisons.

Brahimi Mohamed
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1 Answers1

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I contacted the author of the manual (Mark Allen Weiss) and he informed me that the solution is in the article titled: The Complexity of Heaps written by Svante Carlsson and Jingsen Chen.

Brahimi Mohamed
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  • Although links can be useful, the answer should include the solution. If you don't have it, then it should be just a comment or edit to your question. – trincot Nov 09 '22 at 14:56
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